2 Answers
2

Your mount is a separate creature with its own feat selection, and does not automatically have access to your feats. It cannot use the feats it does not have, and the feats in question do not allow to share their benefits.

As Jeor says, not automatically, but I'd probably allow a player a ride check in order to grant the bonus from the feat to their mount, depending on the feat.

In regards to Dodge and Mobility, I'd probably allow the Dodge bonus on a successful ride check, but not Mobility; the Dodge bonus represents your character's keen reflexes, which you could arguably use to guide your mount out of danger; whereas the Mobility feat is more about your character's personal speed AFAIK.

Mounted Combat feat (taken by a character) already does what you describe - allows you to get your mount out of the harm's way. Still yours is not an unreasonable houserule - the benefit in question is so minor it would hardly affect anything.
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Jeor MattanFeb 26 '13 at 18:27